The Blues owner Roman Abramovich is not willing to offer long-term contracts to stars over the age of 30. Midfielder Lampard, 34, and left-back Cole, 31, have a year left on their contract which ends in the summer.
The England duo will be free to open talks with clubs when the winter transfer window opens on Jan 1. But Chelsea are concerned if the duo leave as free agents next summer.
Lampard is the target for two Chinese clubs and will be offered a lucrative £1m-a-month salary. Former teammate Didier Drogba's club Shanghai Shenhua are also interested in the Chelsea veteran.
Major Soccer League's LA Galaxy are also believed to be interested in Lampard. The Los Angeles club are willing to offer him a long term contract.
Meanwhile, left-back Cole recently rejected a one-year contract extension with Chelsea. The 31-year-old is still at his peak with perfect fitness levels and wants the European Champions to come up with an improved offer.
However, sources close to The Sun said, "Frank and Ashley are still very important to Chelsea but if they stay it will only be on the club's terms."